It seems that the overarching guideline is that questions should be objective enough that they can have a "correct" answer, to avoid being "Primarily Opinon Based." Asking for interpretation of figurative language is generally off-topic, because if there is no one correct answer, it can turn into a competetion for what interpretation is most popular. In this sense, it has less to do with whether the use comes from a song or a poem or prose, but with to what degree the question is about interpretation.
There are some cases where it may be acceptable, as Dan Bron explains:
There is a small niche of acceptable questions of interpretation: those works which have received significant scholarly attention, and therefore credible arguments can be made on the strength of a body of expert literature. Some poems fall into this category.
The challenge with asking for an interpretation of figurative language is described well by Mitch (emphasis mine):
That is the difficulty with general literary interpretation and poetic language of any kind - it often has little to do with the specific language and more to do with culture and art. Figurative meanings are usually repeatable usages in the language, but also often not.
For this reason, questions related to often-used expressions and sayings are completely acceptable, as they relate to how the English language is used. But when a writer uses figurative language to express something in a unique, unprecedented way, this does not necessarily apply.
Consider this question about the figurative use of "having a beef" with something or someone -- an example I chose because I used this figurative phrase in my question:
Do you have a beef with me?
The question is acceptable because the term is not limited to one artist's use and interpretation, but is well grounded enough to be a facet of the English language.
On the other hand, there are some cases where the interpretation has less to do with an understanding of the English language and is more open to interpretation. In such cases, this is off-topic for a site like Stack Exchange, and better suited for a site about poetic interpretation specifically.
With all of this in mind, it seems worth noting that there are no hard-and-fast rules on this site, but as Mitch says, "only suggestions with different strengths." Oftentimes, if a question is interesting and asked in a reasonable manner, the community may give the question the benefit of the doubt for the insight it has the potential to yield, even if the question has other weaknesses, such as opinion bias.
It was suggested that I summarize my understanding based on the comments to form my own answer to my own question. Anyone is welcome (in fact, encouraged) to edit this answer if they see fit and believe there are other important points to take into consideration.